4 Pluses for Developing a Strong Maths Foundation

Mathematics is advancing at a spectacular rate. Mathematics is about pattern and structure. When patterns are found for example, in widely different areas of science and technology, the mathematics of these patterns can be used to explain and control natural happenings and situations. The discipline of mathematics provides a solid foundation to many aspects of daily life, and an insight to the complexities inherent in seemingly simple situations.

Advanced mathematics develops a range of language and insights, which can then be applied to make a crucial contribution to our understanding and appreciation of the world, and our ability to find and make our way in it. It is for this reason that mathematicians are increasingly in demand. [The most recent surveys show graduates in mathematics and computer science are at the top of the earning lists six years after graduation.]

It’s useful to be aware of the wide importance of mathematics; the way in which it has a pervasive influence on our everyday lives, and contributes to the wealth of the country.

The importance of mathematics

The everyday use of arithmetic and the display of information by means of graphs are commonplace and very visible. Advanced mathematics although widely used, is often in an unseen and unadvertised way:

The mathematics of error-correcting codes is applied to CD players and to computers.

The stunning pictures of distant planets, sent by Voyager II could not have had their crispness and quality without advanced mathematics.

Voyager's journey to the planets could not have been calculated without the mathematics of differential equations.

Whenever it is said that advances are made with supercomputers, a mathematical theory would instruct the computer what is to be done, for greater speed and accuracy.

The next generation of software requires the latest methods from what is called category theory, a theory of mathematical structures.

The physical sciences (chemistry, physics, oceanography, astronomy) require mathematics for the development of their own theories.

In ecology, mathematics is used when studying the laws of population change.

Statistics enables the analysis of wide varieties of data.

Statistics is also essential in medicine, for analysing data on the causes of illness and on the use of new drugs.

Travel by aeroplane would not be possible without the mathematics of airflow and of control systems.

Body scanners are the expression of subtle mathematics, discovered in the 19th century, which makes it possible to construct an image of the inside of an object from information on a number of single X-ray views of it. Thus mathematics is often involved in matters of life and death.

These applications have often developed from the study of numbers, symmetry, area and volume, rate of change, shape, dimension, randomness and many others. Mathematics employs the methods of:

precise definitions

careful and rigorous argument

representation of ideas by many methods, including symbols, formulae, pictures and graphics

means of calculation and

gaining precise solutions to clearly stated problems, or clear statements of the limits of knowledge.

These skills are introduced at the simplest levels from primary school through to secondary school education. Mathematics develops the imagination. It trains in clear and logical thought: driven by a need to grasp and manage in the simplest ways - difficult ideas and unsolved problems.

One of the things to look for when choosing a suitable maths course is the amount of personal contact. Mathematics is about learning to do things, and feedback is essential on whether the students’ approaches are the correct and most effective ones.

The use of continuous assessment is also an advantage, since in real life we are tested on the quality of our work, as well as the ability to work efficiently and under pressure. Learning through practise, to produce well thought-out work to a high standard, and communicating it, both in writing and orally are all essential modern-day skills.

Mathematics is a wonderful and exciting subject, the apparently abstract nature of mathematics is one of the reason for its power, as it enables the constructive and creative use of information between apparently diverse situations in mathematical form.